"Let us concentrate on explaining to human beings what we want a computer to do"

Thursday, 16 July 2009

Discovery vs creation

One of the biggest differences between mathematics and programming is the question of authorship. Advances in maths are typically described as discoveries, whereas new software is developed, created or invented. Though programming and mathematics employ similar notations, the uses of these notations are governed by strikingly dissimilar discourses.

Even Kurt Gödel, who's incompleteness theorems are perhaps the most well-known examples of the limitations of mathematics, is widely regarded as a Platonist. He, like many mathematicians, regarded mathematics as more real than the physical world. For a Platonist, theorems are timeless and eternal. Mathematicians' role is to discover and document them as purely as possible. Paul Erdős expressed this sentiment by imagining that the most beautiful proofs came from a book written by God.

The defining characteristic of authorship (as opposed to invention) is that the subjectivity of the author is imprinted on the work. One example of this in mathematics is the calculus. Isaac Newton and Gottfried Leibniz both discovered the calculus, but they approached it in different ways. I would argue that their divergent expressions of the same idea are best understood through the lens of authorship, especially given the importance Leibniz placed on notation and presenting his thoughts for human understanding.

But by and large, mathematicians are better described by Roland Barthes' account of tellers of tales before modern authorship was invented: